A058621 a(n) = 1/2*binomial(2*n,n) - (1+(-1)^n)/4*(binomial(n,floor(n/2)))^2.

0, 1, 1, 10, 17, 126, 262, 1716, 3985, 24310, 60626, 352716, 925190, 5200300, 14168988, 77558760, 217721745, 1166803110, 3355615450, 17672631900, 51855874642, 269128937220, 803232328548, 4116715363800, 12467572005382, 63205303218876, 193873026294052

Offset

0,4

References

A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{i=0..(n-1)/2} binomial(n,i)^2 (see Equation 2 in section 4.2.5 of Prudnikov et al. reference).

Mathematica

Table[1/2 * Binomial[2 n, n] - (1 + (-1)^n)/4 (Binomial[n, n/2])^2, {n, 0, 26}] (* Michael De Vlieger, Aug 25 2015 *)

Prog

(PARI) a(n) = 1/2*binomial(2*n, n) - (1+(-1)^n)/4*(binomial(n, n\2))^2;
(Magma) [1/2*Binomial(2*n, n)-(1+(-1)^n)/4*(Binomial(n, Floor(n/2)))^2: n in [0..30]]; // Vincenzo Librandi, Aug 25 2015

Crossrefs

Sequence in context: A043159 A043939 A351498 * A183229 A219879 A177185

Adjacent sequences: A058618 A058619 A058620 * A058622 A058623 A058624

Keyword

nonn

Author

Yong Kong (ykong(AT)curagen.com), Dec 26 2000

Extensions

Name edited by Michel Marcus, Aug 25 2015

Status

approved